Quantum Mechanics - Study Mode
[#1] If $$sigma $$ is the total cross-section and f(θ), θ being the angle of scattering, is the scattering amplitude for a quantum mechanical elastic scattering by a spherically symmetric potential, then which of the following is true? Note that k is the magnitude of the wave vector along the $${{x08f{hat z}}}$$ direction.
Correct Answer
(C) $$sigma = frac{{4pi }}{k} imes { ext{Imaginary part of }}{left| {fleft( { heta = 0}
ight)}
ight|^2}$$
[#2] Which one of the following relations is true for Pauli matrices σ x , σ y and σ z ?
Correct Answer
(D) σ x σ y = -σ y σ x
[#3] σ i (i = 1, 2, 3) represents the Pauli spin matrices. Which one of the following is not true?
Correct Answer
(D) Det (σ i ) = 1
[#4] A particle is moving in a spherically symmetric potential V(r) = αr 2 , where α is a positive constant. In a stationary state, the expectation value of the kinetic energy $$leftlangle T
ight
angle $$ of the particle is
Correct Answer
(B) $$leftlangle T
ight
angle = 2leftlangle V
ight
angle $$
[#5] The commutator [L x , y], where L x is the x-component of the angular momentum operator and y is the y-component of the position operator, is equal to
Correct Answer
(D) $$ihbar z$$